JP2023085433A - Quantum state conversion method, apparatus, and electronic equipment - Google Patents

Abstract

To provide a quantum state converting method, an apparatus therefor, and electronic equipment therefor which reduce the total costs for quantum state conversion.SOLUTION: A method according to the present invention includes: arranging a first quantum system of a first quantum state including K initial quantum states on the basis of a target conversion relationship; arranging a second quantum system of an auxiliary quantum state on the basis of a second quantum state obtained by embedding a target quantum state into a Hilbert space in the first quantum state on the basis of the first quantum state and a preset quantum state; and on the basis of a quantum state conversion operation in a target conversion relationship, the first quantum system and the second quantum system, performing quantum state transformation on the K initial quantum states and the auxiliary quantum state to obtain the target quantum state and the auxiliary quantum state.SELECTED DRAWING: Figure 1

Description

TECHNICAL FIELD The present disclosure relates to the field of quantum computing technology, in particular to the field of quantum information processing technology, and specifically to a quantum state conversion method, apparatus, and electronic equipment.

Quantum state transformation is one of the fundamental problems in quantum information processing, and a key step in the practical application of quantum technology. In one application scenario, for example, a quantum state purification scenario, two or more initial noisy quantum states can be transformed into target quantum states with relatively low noise by permissible operations, and the target quantum state is It is required that the fidelity between the state and the ideal quantum state reaches a certain threshold.
At present, multi-copy target quantum state transformation strategies are generally used to achieve quantum state transformation, that is, a large number of copies of the initial quantum state are transformed into multiple copies of the target quantum state at once.

The present disclosure provides quantum state conversion methods, devices, and electronic devices.

According to a first aspect of the present disclosure, a method for transforming quantum states is provided, comprising:
constructing a first quantum system in a first quantum state based on a target transformation relation, said first quantum state comprising K initial quantum states, said target transformation relation comprising N said A transformation relationship between an initial quantum state and M target quantum states, wherein the first quantum system includes M first quantum state components, the first quantum state components being superimposed with uniform probability. can obtain the first quantum state, N and M are both integers greater than 1, N is greater than or equal to M, and K is the value obtained by dividing N by M, rounded up to the nearest whole number and
constructing a second quantum system of auxiliary quantum states based on the first quantum state and the second quantum state, the second quantum state transforming the target quantum state to the second quantum state based on a preset quantum state; obtained by embedding in a Hilbert space of one quantum state, wherein the second quantum system includes M−1 first sub-quantum systems, and the first sub-quantum system includes M second quantum a state component, wherein the second quantum state component is the first quantum state or the second quantum state; and the second quantum state component is superimposed with uniform probability to obtain the auxiliary quantum state. what you can do and
performing quantum state transformation on the K initial quantum states and the auxiliary quantum states based on the quantum state transformation operation in the target transformation relation, the first quantum system and the second quantum system; obtaining a target quantum state and the auxiliary quantum state.

According to a second aspect of the present disclosure, an apparatus for transforming quantum states is provided, comprising:
A first construction module configured to construct a first quantum system in a first quantum state based on a target transformation relation, wherein the first quantum state includes K initial quantum states and the target A transformation relation is a transformation relation between the N initial quantum states and M target quantum states, the first quantum system including M first quantum state components, the first quantum state components being , the first quantum state can be obtained by being superposed with uniform probability, N and M are both integers greater than 1, N is greater than or equal to M, and K is N divided by M. a first construction module obtained by rounding up the decimal point based on the value obtained;
a second construction module configured to construct a second quantum system of auxiliary quantum states based on the first quantum state and a second quantum state, wherein the second quantum state is based on a preset quantum state; is obtained by embedding the target quantum state in the Hilbert space of the first quantum state, wherein the second quantum system includes M−1 first sub-quantum systems, and the first sub-quantum system includes M second quantum state components, wherein said second quantum state components are said first quantum state or said second quantum state, and said second quantum state components are superimposed with uniform probability a second construction module capable of obtaining said auxiliary quantum state by
performing quantum state transformation on the K initial quantum states and the auxiliary quantum states based on the quantum state transformation operation in the target transformation relation, the first quantum system and the second quantum system; a quantum state transformation module configured to obtain a target quantum state and the auxiliary quantum state.

According to a third aspect of the present disclosure, an electronic device is provided,
at least one processor; and memory communicatively coupled to the at least one processor;
The memory stores instructions executable by the at least one processor, and when the instructions are executed by the at least one processor, the at least one processor performs any of the methods of the first aspect. can be made
According to a fourth aspect of the present disclosure, there is provided a non-transitory computer-readable storage medium having computer instructions stored thereon, said computer instructions being used to cause said computer to perform any of the methods of the first aspect. .

According to a fifth aspect of the disclosure, there is provided a computer program product, comprising a computer program, for implementing any of the methods of the first aspect when said computer program is executed by a processor.

The technical solution of the present disclosure solves the problem that the transformation cost of multi-copy target quantum state transformation strategy is relatively high, and reduces the overall cost of quantum state transformation.

It is understood that nothing contained in this section is intended to identify key or important features of embodiments of the disclosure, nor is it intended to be used to limit the scope of the disclosure. It should be. Other features of the present disclosure will become easier to understand with the following specification.

The following drawings are used for a better understanding of this approach and do not constitute limitations on the disclosure.

1 is a flow schematic diagram of a quantum state conversion method according to a first embodiment of the present disclosure; FIG. FIG. 1 is 1 of explanatory schematic diagrams of a target conversion relationship; FIG. 4 is an explanatory schematic diagram of transforming a multi-copy target quantum state transformation policy into a single-copy target quantum state transformation strategy with the assistance of a catalyst quantum state; FIG. 2 is an explanatory schematic diagram 2 of the target conversion relationship; It is an explanatory schematic diagram of a first quantum system. It is an explanatory schematic diagram of a second quantum system. FIG. 4 is an explanatory schematic diagram of embedding M target quantum states in a high-dimensional Hilbert space; 1 is an explanatory schematic diagram of a first target quantum system; FIG. FIG. 4 is an explanatory schematic diagram of a second target quantum system; FIG. 4 is an explanatory schematic diagram of a third target quantum system; FIG. 4 is an explanatory schematic diagram of a fourth target quantum system; FIG. 3 is an explanatory schematic diagram of a quantum system obtained by dropping a system embedded in a third target quantum system; 1 is a flow schematic diagram of one specific example quantum state transformation method provided in the present disclosure; FIG. FIG. 4 is a structural schematic diagram of a quantum state transformation device according to a second embodiment of the present disclosure; 1 is a schematic block diagram of an exemplary electronic device for implementing embodiments of the present disclosure; FIG.

The following describes exemplary embodiments of the present application with reference to the drawings, in which various details of embodiments of the disclosure are included for the sake of understanding and are intended to be exemplary only. should be considered. Accordingly, it should be understood by those skilled in the art that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. Also, in the following description, descriptions of well-known functions and structures are omitted for clarity and brevity.

First Embodiment As shown in FIG. 1, the present disclosure provides a quantum state transformation method, including the following steps S101-S103.

In step S101, construct a first quantum system of a first quantum state based on a target transformation relation, said first quantum state comprising K initial quantum states, said target transformation relation comprising N said A transformation relationship between an initial quantum state and M target quantum states, wherein the first quantum system includes M first quantum state components, the first quantum state components being superimposed with uniform probability. Thus, the first quantum state can be obtained.

Here, both N and M are integers greater than 1, N is greater than or equal to M, and K is obtained by dividing N by M and rounding up the decimal point.

In this embodiment, the quantum state transformation method relates to the quantum computing technical field, especially to the quantum information processing technical field, and it can be widely applied to the quantum state purification scene.

For example, in fault-tolerant quantum computation, a purifying operation can be performed on one special quantum state, eg, the magic quantum state, thereby reducing the error in the quantum computation result. Also, for example, in quantum network communication, purifying the entanglement quantum state can enhance the fidelity of information transfer when performing quantum communication using entanglement. That is, quantum state transformations, especially quantum state purification operations, are necessary steps to realize fault-tolerant quantum computing and quantum network communication.

The quantum state transformation method of the embodiments of the present disclosure may be performed by the quantum state transformation apparatus of the embodiments of the present disclosure. The quantum state transformation apparatus of the embodiments of the present disclosure is arranged in any electronic device, thereby performing the quantum state transformation method of the embodiments of the disclosure. The electronic device may be a server or a terminal device, and is not specifically limited here.

The most ideal quantum state purification strategy transforms multiple noisy initial quantum states into one low-noise target quantum state, i.e., realizes a single-copy target quantum state transformation, and simultaneously uses ensure that the number of initial quantum states in Due to the operational limitations allowed to complete the transformation and the threshold requirements for quantum state fidelity after transformation, there is no single-copy target quantum-state transformation strategy. That is, without the assistance of a catalyst quantum state, there is a theoretical limit to the conversion cost of a single-copy target quantum state, below which it may not be possible to complete a conversion.

One popular solution is the multi-copy target quantum state transformation strategy, i.e., simultaneously transforming a large number of copies of the initial quantum state into multiple copies of the target quantum state collectively, thus, the target transformation Realizing the relation, collectively transforming the initial quantum state of N copies into the target quantum state of M copies, i.e., consuming the initial quantum state of N copies, thereby producing M copies can obtain the target quantum state of Here, one copy of the quantum state may refer to the quantum state stored in one collocator, i.e., the initial quantum state stored in the N collocators in the transformation strategy of the multi-copy target quantum state is must be consumed, thereby obtaining M target quantum states.

Such a transformation scheme allows the target quantum state fidelity to reach the threshold requirement, and the average number of initial quantum states used to obtain each target quantum state is relatively small. That is, the conversion can be completed at a relatively low average cost. However, because of the large amount of transformations that need to be performed, the total number of initial quantum states used is relatively large, easily exceeding budgetary control, and the large number of target quantum states obtained is not needed for actual use. can exceed a certain number, causing them to be wasted. For example, in magic quantum state purification used in fault-tolerant quantum computing, a large number of transformations can reduce the average cost, but the total cost is huge.

Thus, the present embodiment provides a strategy for transforming quantum states with the assistance of a catalytic quantum state, and transforms a strategy for transforming any multi-copy target quantum state with the assistance of a catalytic quantum state, i.e., with the assistance of a catalytic quantum state, into A state-assisted single-copy target quantum-state transformation strategy can thus be used to greatly reduce the overall cost of quantum-state transformation.

For example, it is applied to Magick quantum state purification in fault-tolerant quantum computing scene, transforming multi-copy Magick quantum state purification policy into single-copy Magick quantum state purification policy, reducing the purification cost and reducing computational complexity. Accuracy can be improved.

In addition, for example, it is applied to quantum network communication, and the mainstream quantum network architecture adopts quantum teleportation transmission to perform quantum state transmission. A purification operation must be performed on such entangled quantum states first. By transforming the multi-copy entanglement quantum state purification policy into a single-copy entanglement quantum state purification policy, we reduce the cost of the entanglement quantum state purification and improve the accuracy of the entanglement transformation. contribution, thereby further improving the fidelity when the quantum state is transmitted.

との間の忠実度は、１－ε（０≦ε≦１）であり、変換成功確率はｐである。そうすると、本実施例は、触媒量子状態の補助でのシングルコピーターゲット量子状態の変換方策Ｆ´を提供し、Ｋ＝［Ｎ／Ｍ］（即ち、Ｋは、ＮをＭで割った最も小さい正の整数以上である）個のコピーの初期量子状態ρが１個のコピーのターゲット量子状態に変換され得、且つ変換した後で得られるターゲット量子状態と理想量子状態との間の忠実度は１－εであり、成功確率はｐである。 That is, if the target transformation relation holds, the target transformation relation can be realized by a transformation policy F of the multi-copy target quantum state, and the initial quantum state ρ of N copies is transformed into M (M≦N) Convert to the ideal quantum state of the copy, and the target quantum state η ^M obtained by the conversion and the ideal quantum state

is 1−ε (0≦ε≦1) and the conversion success probability is p. The present embodiment then provides a transformation strategy F′ for a single-copy target quantum state with the aid of the catalyst quantum state, where K=[N/M] (i.e., K is the smallest positive value of N divided by M). ) copies of the initial quantum state ρ can be transformed into one copy of the target quantum state, and the fidelity between the target quantum state and the ideal quantum state obtained after transformation is 1 −ε and the probability of success is p.

で表され、実際のシーンにおいてターゲット量子状態間に関連関係が存在することは許容してもよい（即ち、独立で分散するドットでなくてもよい）。 FIG. 2 is a schematic diagram illustrating the target transformation relationship. FIG. represents 100%, and each target quantum state represents successful conversion), and the specific implementation is not limited thereto. Suppose a multi-copy target quantum state transformation policy F exists to transform the initial quantum state ρ of N=15 copies (represented by dots 201) into the target quantum state σ of M=5 copies (represented by dots 202). The target quantum state to be transformed, i.e. obtained in FIG. 2, corresponds to the ideal situation of perfect transformation, i.

, and it may be allowed that there is an association relationship between the target quantum states in the actual scene (ie, not independent and distributed dots).

By way of example, as shown in FIG. 3, a strategy for transforming a multi-copy target quantum state is given, i.e. transforming the initial quantum state of 200 copies into the target quantum state of 100 copies; Embodiments can transform this multi-copy target quantum-state transformation strategy into a single-copy target quantum-state transformation strategy with the assistance of a catalyst quantum state. Specifically, with the help of the catalyst quantum state, two copies of the initial quantum state and the catalyst quantum state are used to complete the quantum state transformation, that is, one copy of the target quantum state is obtained. can be done.

と記録し、ζは、第１量子状態である。図２に示すターゲット変換関係は、図４のように示され得る。ここで、サークル４０１は、第１量子状態を表し、ターゲット変換関係にはＭ組第１量子状態ζが含まれてもよく、それを

で表す。 In a specific implementation, the average number K of initial quantum states used to obtain each target quantum state may be determined if the target transformation relation holds. K is obtained by rounding up to the nearest whole number based on N divided by M, i.e., K=[N/M], with K copies of the quantum state ρ as a set,

and ζ is the first quantum state. The target transformation relationship shown in FIG. 2 can be shown as in FIG. Here the circle 401 represents the first quantum state, and the target transformation relation may include M-tuple first quantum states ζ, which are represented by

Represented by

A first quantum system in a first quantum state can then be constructed, the first quantum system may include M first quantum state components, the M first quantum state components being uniform A first quantum state can be obtained by being superimposed with probability.

In one alternative embodiment, the first quantum state is divided into M components, each component being 1/M of the first quantum states, and the M components are superimposed to obtain the first quantum state. , and a first quantum system can be constructed based on the M components.

In another optional embodiment, taking the first quantum state as a component, the M components can be superimposed with a uniform probability of 1/M to obtain the first quantum state, and based on the M components can be used to construct the first quantum system. As shown in FIG. 5, the column represents the first quantum system and each row of the column represents one first quantum state component.

In step S102, construct a second quantum system of auxiliary quantum states based on a first quantum state and a second quantum state, wherein the second quantum state converts the target quantum state to the first quantum state based on a preset quantum state. embedded in a Hilbert space of quantum states, wherein the second quantum system includes M−1 first sub-quantum systems, and the first sub-quantum system includes M second quantum states wherein the second quantum state component is the first quantum state or the second quantum state, and the second quantum state components are superimposed with uniform probability to obtain the auxiliary quantum state. can be done.

により変換され、つまり、ヒルベルト空間Ｓ^Ｋ－１における零状態を追加することにより、ヒルベルト空間Ｓにおける任意の量子状態Ｗをヒルベルト空間Ｔにおける量子状態

に拡張することができる。Ｗがターゲット量子状態
η
である場合、ε（Ｗ）は、第２量子状態である。 In this step, the second quantum state is obtained by embedding the target quantum state into the Hilbert space of the first quantum state based on the preset quantum state. Here, the preset quantum state may be any one producible quantum state, for example, a zero state that is easy to produce.
In the general case, the initial quantum state ρ and the transformed target quantum state η lie in the same Hilbert space S, ie the corresponding density matrices have the same matrix dimensionality. And the first quantum state is obtained by combining K initial quantum states, i.e., the first quantum state is the quantum state of the high-dimensional Hilbert space ^SK , and the preset quantum state, for example, the zero state The target quantum state of one Hilbert space S is embedded in one high-dimensional Hilbert space T=S ^K based on and the quantum state after embedding is the second quantum state. The specific embedding method is as follows.

that is, any quantum state W in the Hilbert space S is transformed into a quantum state in the Hilbert space T by adding a zero state in the Hilbert space S ^K−1

can be extended to W is the target quantum state η
, then ε(W) is the second quantum state.

The auxiliary quantum state may be referred to as a catalyst quantum state, and can transform a multi-copy target quantum state transformation policy into a single-copy target quantum state transformation policy with the assistance of the catalyst quantum state. Specifically, transforming the first quantum state together with the catalyst quantum state, with the aid of the catalyst quantum state, based on the transformation operation of the quantum states in the target transformation relationship of the multi-copy target quantum state transformation strategy, thereby: Consuming K copies of the initial quantum state may be realized to obtain one copy of the target quantum state. That is, in this embodiment, with the help of the catalyst quantum state, one target quantum state can be obtained only by consuming the initial quantum states stored in the K contributors, thus, a single copy target The constraint that there is a theoretical limit to the cost of transforming quantum states can be broken.

Based on the first quantum state and the second quantum state, a second quantum system of auxiliary quantum states is constructed to assist the transformation of the first quantum state. wherein the constructed second quantum system may include M-1 first sub-quantum systems, and each first sub-quantum system may include M second quantum state components; In this way, the structures of each first sub-quantum system and the first quantum system in the constructed second quantum system are made to be identical, whereby the first quantum state merges with the auxiliary quantum state together. allow it to be converted.

and the second quantum system includes M-1 first sub-quantum systems, and can have M sub-quantum systems after the first quantum system is stitched with the second quantum system; Thereby, performing a quantum state transformation operation in the target transformation relation on M quantum state components (i.e., containing M*K quantum states) in the same dimension of the M sub-quantum systems. can be done. The quantum state transformation operation implements a multi-copy target quantum state transformation strategy, i.e., transforms N initial quantum states (i.e., M*K initial quantum states) into M target quantum states. can be realized.

In a specific construction process, the second quantum state component is set to the first quantum state or the second quantum state, and the second quantum system has at least M-1 second quantum state components in the first quantum state. , so that after the first quantum system is stitched with the second quantum system, the quantum state transformation operation in the target transformation relationship can be performed.

In one alternative embodiment, the M−1 first sub-quantum M−1 quantum state components in the same dimension of the system may be set to the first quantum state. Here, the transform operation may refer to the dimension in which the transformed quantum state component is located or the quantum system in which the quantum state component is located. For example, M−1 quantum state components in the M-th dimension of the M−1 first sub-quantum systems in the second quantum system may be set to the first quantum state.

In one alternative embodiment, the second quantum system may be configured as shown in FIG. 6, where each column represents one first sub-quantum system, i.e. the second The quantum system may include four first sub-quantum systems, each row representing one second quantum state component, i.e. each first sub-quantum system includes five second quantum state components. Alternatively, some of the second quantum state components 601 may be set to the first quantum state, and some of the second quantum state components 602 may be set to the second quantum state. A complete auxiliary quantum state is obtained by superimposing the second quantum state components represented by all rows with uniform probability.

In step S103, quantum state transformation for the K initial quantum states and the auxiliary quantum states based on the quantum state transformation operation in the target transformation relationship, the first quantum system and the second quantum system. to obtain the target quantum state and the auxiliary quantum state.

In this step, the quantum state transformation operation can realize a multi-copy target quantum state transformation strategy, that is, transforming N initial quantum states into M target quantum states.

In one alternative embodiment, if we set a multi-copy target quantum state transformation strategy F such that if N is less than M*K, we drop M*K−N copies of the initial quantum state first, then , operate F on the initial quantum state ρ of the remaining copies (corresponding to operating on the M first quantum states), thereby realizing a transformation operation of the quantum states in the target transformation relation.

In another optional embodiment, the multi-copy target quantum state transformation strategy F may transform M*K initial quantum states, i.e., M first quantum states 701, to obtain target quantum states. , and may be denoted η ^M , and the quantum state may refer to a quantum state in the M Hilbert space S.

と記録してもよい。具体的な埋め込む方式としては、以下の変換

を採用してもよく、即ち、ヒルベルト空間Ｓ^Ｋ－１における零状態を追加することにより、ヒルベルト空間Ｓにおける任意の量子状態Ｗをヒルベルト空間Ｔにおける量子状態

に拡張し、即ち、埋め込んだ後の量子状態は、

である。 As shown in FIG. 7, each Hilbert space S is embedded in one high-dimensional Hilbert space T=S ^K , and the corresponding quantum state after embedding is

may be recorded as As a specific embedding method, the following conversion

that is, any quantum state W in the Hilbert space S can be transformed into a quantum state W in the Hilbert space ^T by adding a zero state in the Hilbert space S

, i.e. the quantum state after embedding is

is.

は、Ｍ個の第２量子状態７０２を含んでもよく、各第２量子状態は、ヒルベルト空間Ｓにおける１つのターゲット量子状態７０２１とヒルベルト空間Ｓにおける２つの零状態７０２２とを含んでもよい。つまり、ターゲット変換関係での量子状態の変換操作とは、Ｍ個の前記第１量子状態をＭ個の第２量子状態に変換することを指してもよい。

may include M second quantum states 702, and each second quantum state may include one target quantum state 7021 in the S Hilbert space and two zero states 7022 in the S Hilbert space. That is, the transformation operation of the quantum states in the target transformation relation may refer to transformation of the M first quantum states into M second quantum states.

A first quantum system and a second quantum system may be stitched together, thereby transforming the first quantum state and the catalyst quantum state together, the stitching scheme moving the first quantum system to the second quantum system. The system may be stitched before, or the first quantum system may be stitched after the second quantum system, and is not specifically limited herein.

A number of operations may be performed based on the first target quantum system obtained by stitching, the operations may include transforming the quantum states in the target transform relation, whereby the target transform relation into a single-copy target quantum-state transformation policy with the assistance of a catalytic quantum state, thereby consuming only K copies of the initial quantum state. makes it possible to obtain one copy of the target quantum state.

Here, transforming the first quantum state and the catalyst quantum state together includes transforming the first quantum state to the target quantum state with the assistance of the catalyst quantum state and transforming the first quantum state to the target quantum state. It may also refer to that the catalyst quantum state can be reduced, ie, that the catalyst quantum state does not change before and after conversion.

In this embodiment, constructing a first quantum system of a first quantum state based on the target transformation relationship, constructing a second quantum system of an auxiliary quantum state based on the first quantum state and the second quantum state, Based on the quantum state transformation operation in the target transformation relationship, the first quantum system and the second quantum system, performing quantum state transformations on the K initial quantum states and the auxiliary quantum states, thereby obtaining the target quantum state and Obtain an auxiliary quantum state. Thus, by using the catalyst quantum state, any multi-copy target quantum state transformation policy is transformed into a catalyst-assisted single-copy target quantum state transformation policy, and the auxiliary quantum state does not change before and after. , which greatly reduces the overall cost of transforming quantum states and expands the range over which quantum states can transform.

Selectably, said step S102 specifically includes:
constructing the second quantum state components in the dimension indicated by each of the states of the M−1 first sub-quantum systems based on the M states of the dimension index to obtain the second quantum system; wherein the dimension index is used to indicate the dimension of the second quantum state component;
when the dimension indicated by the state is i, the second quantum in the i-th dimension of the first i-1 sub-quantum systems among the M-1 first sub-quantum systems; setting the state component as the first quantum state, and determining the second quantum state component in the i-th dimension of Mi sub-quantum systems among the M-1 first sub-quantum systems; as the second quantum state, wherein i is a positive integer less than or equal to M.

In this embodiment, the dimensional index may be an index whose dimensionality is M, which includes M states and may be represented by |i><i|, where 1≤i≤ M−1 and is used to indicate the dimension of the second quantum state component.

の最初のｉ個のヒルベルト空間Ｔにおける量子状態を

と表記し、

はＭ個の量子システムを含み、各量子システムのヒルベルト空間はＴであるので、

を量子状態全体

と称し、

が普通の量子状態（即ち、次元数が１である量子状態）であると約定する。

の定義に基づいて、触媒量子状態を下記の式（１）に示すように構築することができる。

quantum state

Let the quantum states in the first i Hilbert spaces T be

and

contains M quantum systems, and the Hilbert space of each quantum system is T, so

be the whole quantum state

called

is an ordinary quantum state (ie, a quantum state with dimensionality one).

Based on the definition of , the catalyst quantum state can be constructed as shown in equation (1) below.

The second quantum system of auxiliary quantum states constructed in equation (1) above may be as shown in FIG. - One quantum system T (i.e., the first sub-quantum system represented by a sequence) and a classical system of dimension M (i.e., a system of second quantum state components of dimension M) Each row represents one quantum state component of the auxiliary quantum state, and the complete catalytic quantum state is obtained by overlapping with uniform probability the quantum state components represented by all the rows. Here, a quantum system T can represent a quantum system whose quantum states are located in the Hilbert space T.

に設定し、即ち、Ｍ－１個の第１サブ量子システムにおける最初のｉ―１個のサブ量子システムの、ｉ個の目の次元での各第２量子状態成分をいずれも第１量子状態に設定し、残りのサブ量子システムは第２量子状態

であり、即ち、Ｍ－１個の第１サブ量子システムにおける最後のＭ－ｉ個のサブ量子システムの、ｉ個の目の次元での各第２量子状態成分をいずれも第２量子状態に設定し、古典システムの状態を｜ｉ〉〈ｉ|に設定し、すべての異なる１≦ｉ≦Ｍに対応する第２量子状態成分を均一な確率で重畳し、それにより、補助量子状態ωを得ることができる。 A specific construction method will be described as follows. For a given dimensional index i (1≦i≦M), let the first i−1 subquantum systems in the M−1 first subquantum systems be the first quantum state

, that is, each second quantum state component in the i-th dimension of the first i−1 sub-quantum systems in the M−1 first sub-quantum systems is set to the first quantum state , and the rest of the sub-quantum systems are in the second quantum state

That is, each second quantum state component in the i-th dimension of the last Mi sub-quantum systems in the M-1 first sub-quantum systems is the second quantum state , set the state of the classical system to |i><i|, and superimpose the second quantum state components corresponding to all different 1≦i≦M with uniform probability, so that the auxiliary quantum state ω is Obtainable.

In the present embodiment, constructing the second quantum state components in the dimension indicated by each of the states of the M−1 first sub-quantum systems based on the M states of the dimension index; Obtaining a two-quantum system, the dimension index is used to indicate the dimension of the second quantum state component. Thus, the construction of catalytic quantum states can be realized.

Optionally, the second quantum system includes M-1 target quantum state components, the M-1 target quantum state components located in the same dimension, and the M-1 target quantum state components. The quantum state components are the same, the target quantum state component is the first quantum state, and step S103 specifically includes:
stitching the first quantum system and the second quantum system to obtain a first target quantum system, wherein in the first target quantum system the first quantum system is before the second quantum system; be arranged in
performing the quantum state transformation operation on M third quantum state components to obtain a second target quantum system, wherein the M third quantum state components are the first quantum state components; and M−1 of the target quantum state components, wherein the quantum state transformation operation comprises transforming M of the first quantum states into M of the second quantum states;
performing a quantum state swap operation on the second target quantum system to obtain a third target quantum system, wherein the second sub-quantum systems in the third target quantum system comprise M the second comprising quantum states, wherein the second sub-quantum system is arranged before M-1 third sub-quantum systems, the third sub-quantum systems being the second sub-quantum systems in the third target quantum system; is another sub-quantum system other than, and the M-1 third sub-quantum systems and the M-1 first sub-quantum systems are the same;
performing a reduction operation on the second sub-quantum system to obtain the target quantum state;
obtaining the auxiliary quantum state by superposing the quantum state components of each dimension in the M−1 third sub-quantum systems with uniform probability.

In this embodiment, the second quantum system may include M−1 target quantum state components, the M−1 target quantum state components are located in the same dimension, and the M−1 target quantum state components The quantum state components are identical and the target quantum state component is the first quantum state.

で表される。 As shown in FIG. 6, the M−1 second quantum state components in the Mth dimension in the second quantum system are all first quantum states. The following catalyst quantum states will be described in detail with reference to FIG. 6 as an example, with the help of the catalyst quantum states, to transform the K initial quantum states.
stitching the first quantum system and the second quantum system to obtain a first target quantum system, arranging the first quantum system before the second quantum system in the stitching process;

is represented by

As for the first target quantum system, as shown in FIG. 8, the sub-quantum system to the left of the dashed line is the first quantum system, and the sub-quantum system to the right of the dashed line is the second quantum system. The first target quantum system may include M quantum systems Tt and one classical system of dimension M.

と表され、ここで、ｉｄは恒等変換であり、即ち、操作しないことであり、Ｆは、マルチコピーターゲット量子状態の変換方策であり、Ｍ＊Ｋ＞Ｎである場合、Ｍ＊Ｋ－Ｎ個のコピーの初期量子状態をまずドロップし、Ｆを残りのＮ個のコピーの初期量子状態ρに作用することができる。即ち、制御ビットがＭである場合、被制御ビットにターゲット変換関係での量子状態の変換操作を施し、そうではない場合、操作しない。 Thereafter, a control operation is performed on the first target quantum system with one classical system as the control bit and the quantum system as the controlled bit to obtain the second target quantum system. Specifically, the control operation is

where id is the identity transformation, i.e., do not manipulate, F is the transformation policy of the multi-copy target quantum state, and if M*K>N, then M*K− We can drop the initial quantum states of N copies first and let F act on the initial quantum states ρ of the remaining N copies. That is, if the control bit is M, the controlled bit is subjected to the transformation operation of the quantum state in the target transformation relationship; otherwise, the operation is not performed.

Since the transformation policy F of the multi-copy target quantum state has a certain probability of success or failure, when applying F, if the experiment fails, recreate the catalyst quantum state and transform the quantum state until the experiment succeeds. again.

The quantum state after a successful experiment is denoted by ν ₁ , and the second target quantum system in that quantum state ν ₁ is M It can be seen from FIG. 9 that the quantum state components have already been successfully transformed from M first quantum states to M second quantum states, where M=5.

A quantum state swap operation can then be performed on the second target quantum system to obtain a third target quantum system. Here, the quantum state exchange operation may include a dimension exchange operation of quantum state components and/or a quantum system exchange operation of quantum states. and thereby transforming a quantum state component from one dimension to another dimension, and a quantum system exchange operation of quantum states means exchanging a quantum system of quantum states, thereby transforming a quantum state into one dimension. Refers to transforming a quantum system into another quantum system.

The third target quantum system may include a second sub-quantum system and a third sub-quantum system, the second sub-quantum system being the frontmost quantum system, and the third sub-quantum system being the second sub-quantum system. Arranged after the sub-quantum systems, the third target quantum system may include M-1 third sub-quantum systems.

The purpose of the quantum state exchange operation is to replace the quantum system (the quantum system of the initial quantum state with K array positions) by the dimension exchange operation of the quantum state components and/or the quantum system exchange operation of the quantum state. The M quantum state components contained in the system, ie corresponding to the first quantum system, are transformed into M second quantum states to obtain a second sub-quantum system.

In one alternative embodiment, a quantum state exchange operation can result in a third target quantum system, and as shown in FIG. , and the second quantum state 1002 may include a target quantum state 10021 and an embedded preset quantum state 10022 .

Since the second quantum state is obtained by embedding the target quantum state into the Hilbert space of the first quantum state based on the preset quantum state, thus, the second sub-quantum system, i.e., the M second quantum states, is obtained. A reduction operation can be performed on a quantum state to obtain a quantum system in a target quantum state, and the target quantum state can be obtained based on the quantum system in the target quantum state. Here, the reduction operation may refer to dropping or deleting the preset quantum state at the embedding position in the second quantum state.

A target quantum state can be obtained and an auxiliary quantum state can be reduced by performing a quantum state conversion operation and a quantum state exchange operation on the first target quantum system. As shown in FIG. 10, the third target quantum system further includes a quantum system 1003 in the second quantum system array position of the auxiliary quantum state, i.e. M−1 third sub-quantum systems, the third The quantum system 1003 at the second quantum system alignment position of the auxiliary quantum state in the target quantum system and the second quantum system of the auxiliary quantum state shown in FIG. 6 are identical. In this way, by superposing the quantum state components of each dimension in the M−1 third sub-quantum systems with uniform probability, an auxiliary quantum state can be obtained, which can be used repeatedly in this way. .

In this embodiment, stitching the first quantum system and the second quantum system to obtain a first target quantum system, performing a quantum state transformation operation on the M third quantum state components, Obtaining a second target quantum system, performing a quantum state exchange operation on the second target quantum system, obtaining a third target quantum system, wherein a second sub-quantum system in the third target quantum system comprises M th A reduction operation is performed on the second sub-quantum system comprising two quantum states to obtain a target quantum state. Thus, based on stitching the first quantum system and the second quantum system to obtain the first target quantum system, a series of operations (quantum states in target transformation relation transformation operation, quantum state exchange operation and reduction operation) to transform the quantum system corresponding to the K initial quantum states at the array position, i.e. the first quantum system, into the quantum system of the target quantum state capable of transforming, thereby realizing, with the aid of the catalyst quantum state, transforming one copy of the target quantum state by consuming K copies of the initial quantum state; Thus, the overall cost of transforming quantum states is greatly reduced.

Optionally, performing a quantum state swap operation on the second target quantum system to obtain a third target quantum system comprises:
taking a dimension as a reference and performing a first rotation operation on quantum state components of each dimension in the second target quantum system to obtain a fourth target quantum system;
taking a sub-quantum system as a reference and performing a second rotation operation on each sub-quantum system in the fourth target quantum system to obtain the third target quantum system.

In this embodiment, the quantum state exchange operation may include a first rotation operation and a second rotation operation, the first rotation operation may correspond to the dimension exchange operation of the quantum state components, and the quantum state components may be Used to transform from one dimension to another, the second rotation operation may correspond to a quantum system exchange operation of quantum states, transforming quantum states from one quantum system to another. used for

Here, rotation may refer to sequentially transforming the quantum state components until the transformation of all quantum components is completed, and taking the dimension as a reference refers to transforming the quantum state components of one dimension to another. Refers to collectively transforming into dimensions, and referencing a subquantum system refers to collectively transforming all quantum state components in a quantum state from one subquantum system to another. .

The first rotation operation may include one, two or more rotations, the order of rotation may be in ascending order of dimension, but may also be in order from largest to smallest, and the second rotation operation may include: One, two or more rotations may be included, and the order of rotation may follow the ordering order of the sub-quantum systems from front to back, or may follow the ordering order from back to front, neither of which is specified here. not strictly limited.

A fourth target quantum system may be obtained by performing a first rotation operation on the quantum state components of each dimension in the second target quantum system with an arbitrary rotation step size on the basis of the dimension. In one alternative embodiment, the rotation step size may be 1, the first rotation operation may include one rotation, and the rotation order may follow the ascending order of the dimensions.

Taking the sub-quantum system as a reference, performing a second rotation operation on each sub-quantum system in the fourth target quantum system with an arbitrary rotation step size to obtain a third target quantum system. In one alternative embodiment, the rotation step size may be 1, the second rotation operation may comprise one rotation, and the rotation order is according to the front-to-back ordering order of the sub-quantum system. good too.

The first rotation operation may be performed by applying a unitary transformation to the classical system in the second target quantum system. A different sub-quantum system in the fourth target quantum system may be exchanged via a swap (SWAP) gate, thereby performing a second rotation operation.

In this embodiment, by the first rotation operation and the second rotation operation, M quantum state components included in the quantum system arranged first are converted into M second quantum states, and the second sub-quantum system can be obtained, and the realization by the rotation scheme is relatively simple.

Selectably, by dimension, performing a first rotation operation on quantum state components of each dimension in said second target quantum system to obtain a fourth target quantum system comprises:
Rotating quantum state components of each dimension in the second target quantum system with a rotation step size of 1 in ascending order of dimensions to obtain a fourth target quantum system.

In this embodiment, the rotation order is according to the ascending order of the dimensions, the rotation step size is 1, and only one rotation may be performed, and the unitary transformation is realized by adopting the following equation (2) be able to.

In the above equation (2), the quantum state ν ₁ , ie the number of classical systems in the second target quantum system, is rotated, ie for all 1≦i≦M−1, |i> We may transform <i| to |i+1><i+1| and |M><M| to |1><1|, denoting the quantum state after rotation as _ν2 .

Taking FIG. 9 as an example, after executing the unitary transformation shown in the above equation (2), all the rows in FIG. 9 are rotated, the last row is moved to the first row, and the first row is moved to We may move to line 2 and by analogy thus obtain a fourth target quantum system as shown in FIG.

In this embodiment, according to the ascending order of the dimensions, the rotation step size is 1, and only the first rotation operation of the one-time rotation is performed, further simplifying the quantum state exchange operation, so that the quantum state transformation processing can be simplified.

Optionally, taking said sub-quantum system as a reference and performing a second rotation operation on each sub-quantum system in said fourth target quantum system to obtain said third target quantum system comprises:
Rotating each sub-quantum system in the fourth target quantum system with a rotation step size of 1 according to the front-to-back arrangement order of the sub-quantum systems to obtain the third target quantum system.

In this embodiment, the rotation order is according to the front-to-back arrangement order of the sub-quantum systems, the rotation step size is 1, only one rotation is performed, and the quantum state ν ₂ , that is, the fourth target quantum system , and set the numbers of the subquantum systems to be 1, 2, . The quantum state in system i may be transformed into sub-quantum system i+1, and the quantum state in sub-quantum system M may be transformed into sub-quantum system 1 . A specific rotation scheme can be realized by performing a SWAP gate between adjacent sub-quantum systems, denoting the quantum state after rotation as _ν3 .

Taking FIG. 11 as an example, rotate the sub-quantum systems for the fourth target quantum system obtained in FIG. , moving the first column to the second column, and thus analogizing, we obtain the third target quantum system as shown in FIG.

In this embodiment, according to the front-to-back arrangement order of the sub-quantum system, the rotation step size is 1, and only the second rotation operation of one rotation is performed, thereby further simplifying the quantum state exchange operation. , thereby simplifying the process of transforming quantum states.

Selectably performing a reduction operation on the second sub-quantum system to obtain the target quantum state comprises:
removing the preset quantum states embedded in the M second quantum states to obtain a fourth sub-quantum system, the fourth sub-quantum system including M third quantum states; the third quantum state is a quantum state obtained after deleting the preset quantum state;
convolving the M third quantum states with uniform probability to obtain the target quantum state.

In this embodiment, processing may be performed for each second quantum state in the second sub-quantum system in the third target quantum system, specifically dropping the preset quantum state embedded in each second quantum state. ie, drop the embedded system S ^K-1 in the first quantum system T and obtain the fourth sub-quantum system.

As shown in FIG. 12, drop the embedded system in the one-eyed quantum system T of the quantum state obtained in FIG. to obtain a fourth sub-quantum system, which may include M third quantum states 1201, and by superposing the M third quantum states with uniform probability, 1 output the quantum state in the 1-th quantum system, i.e. the fourth sub-quantum system, said quantum state is the target quantum state, thus the quantum state in the 1-th quantum system is a single copy be the target quantum state of . Then, a transformation of a single-copy target quantum state with the aid of the catalyst quantum state can be realized, i.e., K copies of the initial quantum state can be consumed to obtain one copy of the target quantum state.

The following describes in detail the quantum state transformation strategy provided in this embodiment for one specific example. As shown in FIG. 13, the example includes the following steps 1302-1309.
In step S1301, input a transformation strategy for a multi-copy target quantum state, whose parameters may include F, N, M, ρ, σ, ε, p, and so on.

In step S1302, K is calculated and the initial quantum states are combined to construct a first quantum system in the first quantum state, as shown in FIG.

In step S1303, the target quantum state is embedded in the Hilbert space T as shown in FIG.

In step S1304, a catalyst quantum state is constructed to obtain a second quantum system of auxiliary quantum states shown in FIG.

In step S1305, after stitching the first quantum system in the first quantum state and the second quantum system in the auxiliary quantum state shown in FIG. 5 to obtain the first target quantum system shown in FIG. A quantum state transformation operation is performed on the quantum system to obtain a second target quantum system shown in FIG.

In step S1306, the rotation step size is set to 1 and the quantum state components of each dimension in the second target quantum system are rotated in ascending order of dimensions to obtain the fourth target quantum system shown in FIG.

In step S1307, according to the arrangement order of the sub-quantum systems from front to back, with a rotation step size of 1, each sub-quantum system in the fourth target quantum system is rotated, and the third target quantum system shown in FIG. 10 is rotated. get

At step S1308, the embedded quantum system is dropped to obtain the quantum system shown in FIG.

In step S1309, based on the quantum system shown in FIG. 12, the single-copy target quantum state and the auxiliary quantum state are output by superposition with uniform probability.

Second Embodiment As shown in FIG. 14, the present disclosure provides a quantum state transformation device 1400,
A first construction module 1401 configured to construct a first quantum system in a first quantum state based on a target transformation relation, said first quantum state comprising K initial quantum states, said A target transformation relation is a transformation relation between the N initial quantum states and M target quantum states, the first quantum system includes M first quantum state components, and the first quantum state components can obtain the first quantum state by being superimposed with a uniform probability, N and M are both integers greater than 1, N is greater than or equal to M, and K is N with M a first construction module 1401 obtained by rounding up the decimal point based on the divided value;
A second construction module 1402 configured to construct a second quantum system of auxiliary quantum states based on the first quantum state and the second quantum state, wherein the second quantum state is a preset quantum state. The second quantum system is obtained by embedding the target quantum state in the Hilbert space of the first quantum state based on The system includes M second quantum state components, wherein the second quantum state components are the first quantum state or the second quantum state, and the second quantum state components are superimposed with uniform probability. a second construction module 1402 capable of obtaining said auxiliary quantum state by
performing quantum state transformation on the K initial quantum states and the auxiliary quantum states based on the quantum state transformation operation in the target transformation relation, the first quantum system and the second quantum system; a quantum state transformation module 1403 configured to obtain a target quantum state and the auxiliary quantum state.

Optionally, said second construction module 1402 specifically:
constructing the second quantum state components in the dimension indicated by each of the states of the M−1 first sub-quantum systems based on the M states of the dimension index to obtain the second quantum system; wherein the dimension index is used to indicate the dimension of the second quantum state component;
when the dimension indicated by the state is i, the second quantum in the i-th dimension of the first i-1 sub-quantum systems among the M-1 first sub-quantum systems; setting the state component as the first quantum state, and determining the second quantum state component in the i-th dimension of Mi sub-quantum systems among the M-1 first sub-quantum systems; is set as the second quantum state, and i is a positive integer less than or equal to M.

Optionally, the second quantum system includes M-1 target quantum state components, the M-1 target quantum state components located in the same dimension, and the M-1 target quantum state components. the quantum state components are the same, the target quantum state component is the first quantum state, and the quantum state transformation module 1403 comprises:
a stitching sub-module configured to stitch the first quantum system and the second quantum system to obtain a first target quantum system, wherein in the first target quantum system the first quantum system is , a stitching sub-module arranged in front of the second quantum system;
a first manipulation sub-module configured to perform a transformation operation of said quantum state on M third quantum state components to obtain a second target quantum system, wherein said M third quantum states; The components include the first quantum state component and the M−1 target quantum state components, and the quantum state transform operation transforms the M first quantum states into M the second quantum states. a first manipulation sub-module comprising:
a second manipulation sub-module configured to perform a quantum state exchange operation on the second target quantum system to obtain a third target quantum system, wherein a second sub-quantum in the third target quantum system; The system includes M said second quantum states, said second sub-quantum system being arranged in front of M-1 third sub-quantum systems, said third sub-quantum systems being aligned with said third target A second operation sub-quantum system other than the second sub-quantum system in the quantum system, wherein the M-1 third sub-quantum systems and the M-1 first sub-quantum systems are the same a module;
a third manipulation sub-module configured to perform a reduction operation on the second sub-quantum system to obtain the target quantum state;
a convolution sub-module configured to convolute the quantum state components of each dimension in the M−1 third sub-quantum systems with uniform probability to obtain the auxiliary quantum state.

Selectably, the second manipulation sub-module comprises:
a first operation unit configured to take a dimension as a reference and perform a first rotation operation on quantum state components of each dimension in the second target quantum system to obtain a fourth target quantum system;
a second operation unit configured to take a sub-quantum system as a reference and perform a second rotation operation on each sub-quantum system in the fourth target quantum system to obtain the third target quantum system. .

Selectably, the first operating unit specifically:
It is configured to rotate the quantum state components of each dimension in the second target quantum system according to the ascending order of the dimensions with a rotation step size of 1 to obtain a fourth target quantum system.

Selectably, the second operating unit specifically:
rotating each sub-quantum system in the fourth target quantum system with a rotation step size of 1 according to the front-to-back arrangement order of the sub-quantum systems to obtain the third target quantum system; .

Selectably, the third manipulation sub-module specifically:
removing the preset quantum states embedded in the M second quantum states to obtain a fourth sub-quantum system, the fourth sub-quantum system including M third quantum states; the third quantum state is a quantum state obtained after deleting the preset quantum state;
convolving the M third quantum states with uniform probability to obtain the target quantum state.

The quantum state transformation device 1400 provided in the present disclosure can realize each process implemented in the embodiments of the quantum state transformation method, and achieve the same beneficial effect, to avoid duplication. , the description is omitted here.

In the technical solution of the present disclosure, the acquisition, storage, use, processing, transmission, provision, disclosure, etc. of the user's personal information conforms to the relevant laws and regulations and is contrary to public order and morals. isn't it.

Based on the embodiments of the disclosure, the disclosure further provides an electronic device, a readable storage medium, and a computer program product.

FIG. 15 shows a schematic block diagram of an exemplary electronic device 600 that may be used to implement embodiments of the present disclosure. Electronic equipment is intended to represent various forms of digital computers such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers and other suitable computers. . Electronic devices can also represent various forms of mobile devices such as personal digital assistants, cell phones, smart phones, wearable devices and other similar computing devices. It should be noted that the components, their connections and relationships, and their functionality shown in this disclosure are exemplary only and are not intended to limit the implementation of the disclosure as described and/or claimed in this disclosure. .

As shown in FIG. 15, electronic device 1500 can perform various suitable operations by computer programs stored in read only memory (ROM) 1502 or loaded into random access memory (RAM) 1503 from storage unit 1508 . and a computing unit 1501 capable of performing processing. Random access memory 1503 can further store various programs and data necessary for the operation of electronic device 1500 . Calculation unit 1501 , ROM 1502 and RAM 1503 are connected to each other via bus 1504 . Input/output (I/O) interface 1505 is also connected to bus 1504 .

In the electronic device 1500, an input unit 1506 such as a keyboard, mouse, etc., an output unit 1507 such as various types of displays, speakers, etc., a storage unit 1508 such as a magnetic disk, an optical disk, etc., a network card, a modem, a wireless communication transceiver, etc. A plurality of components are connected to the I/O interface 1505, including the communication unit 1509 of the . Communications unit 1509 enables electronic device 1500 to interact information or data with other devices over computer networks such as the Internet and/or various telecommunications networks.

Computing unit 1501 may be various general purpose and/or special purpose processing components having processing and computing capabilities. Some examples of computational units 1501 include central processing units (CPUs), graphics processing units (GPUs), various dedicated artificial intelligence (AI) computational chips, various computational units that run machine learning model algorithms, digital Including, but not limited to, signal processors (DSPs), and any suitable processors, controllers, microcontrollers, and the like. Computing unit 1501 performs various methods and processes, such as the quantum state transformation method described above. For example, in some embodiments, quantum state transformation methods may be implemented as a computer software program tangibly contained in a machine-readable medium, such as storage unit 1508 . In some embodiments, part or all of the computer program may be loaded and/or installed in electronic device 1500 via ROM 1502 and/or communication unit 1509 . When the computer program is loaded into RAM 1503 and executed by computing unit 1501, it is capable of performing one or more steps of the quantum state transformation method described above. Alternatively, in other embodiments, computation unit 1501 may be configured to perform quantum state transformation methods in any other suitable manner (eg, by firmware).

In this disclosure, the various embodiments of the systems and techniques described above include digital electronic circuit systems, integrated circuit systems, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs) ), system-on-chip (SOC), complex programmable logic device (CPLD), computer hardware, firmware, software, and/or combinations thereof. Each of these embodiments may be implemented in one or more computer programs, which may be executed and/or interpreted in a programmable system including at least one programmable processor; The processor may be a dedicated or general purpose programmable processor, capable of receiving data and instructions from the storage system, at least one input device and at least one output device, and transmitting data and instructions to the storage system, the at least one transmitting to one input device and the at least one output device.

Program code to implement the methods of the present disclosure may be written in any combination of one or more programming languages. These program codes may be provided to a processor or controller of a general purpose computer, special purpose computer, or other programmable data processing apparatus, and when executed by the processor or controller, these program codes may be represented by flowchart illustrations and/or block diagrams. The functions/operations specified in are performed. The program code may run entirely on the device, partially on the device, or partially on the device and partially on the remote device as a stand-alone software package. or can be performed entirely on a remote device or server.

In the context of this disclosure, a machine-readable medium may be a tangible medium and includes a program for use by or in conjunction with an instruction execution system, apparatus or device. or can be stored. A machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media may include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or instruments, or any suitable combination thereof. More specific examples of machine-readable storage media include electrical connections based on one or more cables, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable Read only memory (EPROM or flash memory), optical fiber, compact disc read only memory (CD-ROM), optical storage, magnetic storage, or any suitable combination thereof may be included.

To provide user interaction, the systems and techniques described herein use a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) to display information to the user, a keyboard and pointing device. It can be implemented on a computer with a device (eg, a mouse or trackball), and a user can provide input to the computer via the keyboard and the pointing device. Other types of devices can be used to provide interaction with the user. For example, the feedback provided to the user may be any form of sensing feedback, e.g., visual, auditory, or tactile feedback, and any form of input from the user, including sound, audio, or tactile input. may receive input from

The systems and techniques described herein may be implemented in computing systems that include background components (e.g., data servers) or may be implemented in computing systems that include middleware components (e.g., application servers). , or on a computing system that includes front-end components (e.g., a user computer having a graphical user interface or web browser), through which a user can interact with the systems and techniques described herein. or may be implemented in a computing system that includes any combination of such background, middleware, or front-end components. Further, each component of the system may be connected by digital data communication via any form or medium such as a communication network. Communication networks include local area networks (LAN), wide area networks (WAN), the Internet, and the like.

The computer system can include clients and servers. A client and server are typically remote from each other and interact through a communication network. The relationship of client and server is created by computer programs running on the corresponding computers and each having a client-server relationship. The server may be a cloud server, a server of a distributed system, or a server combined with a blockchain.

It should be appreciated that steps may be rearranged, added or deleted from the various forms of flow described above. For example, each step described in this application can be performed in parallel, in sequence, or in a different order, as long as the desired result of the technical solution disclosed in this application can be achieved. may be The specification does not limit it here.

The above specific embodiments are not intended to limit the protection scope of the present application. It should be understood by those skilled in the art that various modifications, combinations, subcombinations, and substitutions can be made depending on design requirements and other factors. Any modification, equivalent replacement, improvement, etc. without departing from the spirit and principle of this disclosure shall fall within the protection scope of this disclosure.

Claims (17)

A quantum state transformation method comprising:
constructing a first quantum system in a first quantum state based on a target transformation relation, said first quantum state comprising K initial quantum states, said target transformation relation comprising N said A transformation relationship between an initial quantum state and M target quantum states, wherein the first quantum system includes M first quantum state components, the first quantum state components being superimposed with uniform probability. can obtain the first quantum state, N and M are both integers greater than 1, N is greater than or equal to M, and K is the value obtained by dividing N by M, rounded up to the nearest whole number and
constructing a second quantum system of auxiliary quantum states based on the first quantum state and the second quantum state, the second quantum state transforming the target quantum state to the second quantum state based on a preset quantum state; obtained by embedding in a Hilbert space of one quantum state, wherein the second quantum system includes M−1 first sub-quantum systems, and the first sub-quantum system includes M second quantum a state component, wherein the second quantum state component is the first quantum state or the second quantum state; and the second quantum state component is superimposed with uniform probability to obtain the auxiliary quantum state. what you can do and
performing quantum state transformation on the K initial quantum states and the auxiliary quantum states based on the quantum state transformation operation in the target transformation relation, the first quantum system and the second quantum system; obtaining a target quantum state and the auxiliary quantum state. Constructing a second quantum system of auxiliary quantum states based on the first quantum state and the second quantum state includes:
constructing the second quantum state components in the dimension indicated by each of the states of the M−1 first sub-quantum systems based on the M states of the dimension index to obtain the second quantum system; wherein the dimension index is used to indicate the dimension of the second quantum state component;
when the dimension indicated by the state is i, the second quantum in the i-th dimension of the first i-1 sub-quantum systems among the M-1 first sub-quantum systems; setting the state component as the first quantum state, and determining the second quantum state component in the i-th dimension of Mi sub-quantum systems among the M-1 first sub-quantum systems; as the second quantum state, wherein i is a positive integer less than or equal to M. The second quantum system includes M−1 target quantum state components, the M−1 target quantum state components are located in the same dimension, and the M−1 target quantum state components are are the same, and the target quantum state component is the first quantum state;
performing quantum state transformation on the K initial quantum states and the auxiliary quantum states based on the quantum state transformation operation in the target transformation relation, the first quantum system and the second quantum system; Obtaining a target quantum state and said auxiliary quantum state comprises:
stitching the first quantum system and the second quantum system to obtain a first target quantum system, wherein in the first target quantum system the first quantum system is before the second quantum system; be arranged in
performing the quantum state transformation operation on M third quantum state components to obtain a second target quantum system, wherein the M third quantum state components are the first quantum state components; and M−1 of the target quantum state components, wherein the quantum state transformation operation comprises transforming M of the first quantum states into M of the second quantum states;
performing a quantum state swap operation on the second target quantum system to obtain a third target quantum system, wherein the second sub-quantum systems in the third target quantum system comprise M the second comprising quantum states, wherein the second sub-quantum system is arranged before M-1 third sub-quantum systems, the third sub-quantum systems being the second sub-quantum systems in the third target quantum system; is another sub-quantum system other than, and the M-1 third sub-quantum systems and the M-1 first sub-quantum systems are the same;
performing a reduction operation on the second sub-quantum system to obtain the target quantum state;
2. The method of claim 1, further comprising: convolving quantum state components of each dimension in the M-1 third sub-quantum systems with uniform probability to obtain the auxiliary quantum state. performing a quantum state swap operation on the second target quantum system to obtain a third target quantum system;
taking a dimension as a reference and performing a first rotation operation on the quantum state components of each dimension in the second target quantum system to obtain a fourth target quantum system;
4. The method of claim 3, comprising taking a sub-quantum system as a reference and performing a second rotation operation on each sub-quantum system in the fourth target quantum system to obtain the third target quantum system. Taking a dimension as a reference, performing a first rotation operation on quantum state components of each dimension in the second target quantum system to obtain a fourth target quantum system includes:
5. The method of claim 4, comprising rotating the quantum state components of each dimension in the second target quantum system with a rotation step size of 1 according to ascending order of dimensions to obtain a fourth target quantum system. taking a sub-quantum system as a reference and performing a second rotation operation on each sub-quantum system in the fourth target quantum system to obtain the third target quantum system;
rotating each sub-quantum system in the fourth target quantum system with a rotation step size of 1 according to the front-to-back arrangement order of the sub-quantum systems to obtain the third target quantum system. 4. The method described in 4. performing a reduction operation on the second sub-quantum system to obtain the target quantum state;
removing the preset quantum states embedded in the M second quantum states to obtain a fourth sub-quantum system, the fourth sub-quantum system including M third quantum states; the third quantum state is a quantum state obtained after deleting the preset quantum state;
4. The method of claim 3, comprising convolving the M third quantum states with uniform probability to obtain the target quantum state. A quantum state converter, comprising:
A first construction module configured to construct a first quantum system in a first quantum state based on a target transformation relation, wherein the first quantum state includes K initial quantum states and the target A transformation relation is a transformation relation between the N initial quantum states and M target quantum states, the first quantum system including M first quantum state components, the first quantum state components being , the first quantum state can be obtained by being superposed with uniform probability, N and M are both integers greater than 1, N is greater than or equal to M, and K is N divided by M. a first construction module obtained by rounding up the decimal point based on the value obtained;
a second construction module configured to construct a second quantum system of auxiliary quantum states based on the first quantum state and a second quantum state, wherein the second quantum state is based on a preset quantum state; is obtained by embedding the target quantum state in the Hilbert space of the first quantum state, wherein the second quantum system includes M−1 first sub-quantum systems, and the first sub-quantum system includes M second quantum state components, wherein said second quantum state components are said first quantum state or said second quantum state, and said second quantum state components are superimposed with uniform probability a second construction module capable of obtaining said auxiliary quantum state by
performing quantum state transformation on the K initial quantum states and the auxiliary quantum states based on the quantum state transformation operation in the target transformation relation, the first quantum system and the second quantum system; a quantum state transformation module configured to obtain a target quantum state and the auxiliary quantum state. Specifically, the second construction module includes:
constructing the second quantum state components in the dimension indicated by each of the states of the M−1 first sub-quantum systems based on the M states of the dimension index to obtain the second quantum system; wherein the dimension index is used to indicate the dimension of the second quantum state component;
when the dimension indicated by the state is i, the second quantum in the i-th dimension of the first i-1 sub-quantum systems among the M-1 first sub-quantum systems; setting the state component as the first quantum state, and determining the second quantum state component in the i-th dimension of Mi sub-quantum systems among the M-1 first sub-quantum systems; as the second quantum state, wherein i is a positive integer less than or equal to M. The second quantum system includes M−1 target quantum state components, the M−1 target quantum state components are located in the same dimension, and the M−1 target quantum state components are are identical, the target quantum state component is the first quantum state, and the quantum state transformation module comprises:
a stitching sub-module configured to stitch the first quantum system and the second quantum system to obtain a first target quantum system, wherein in the first target quantum system the first quantum system is , a stitching sub-module arranged in front of the second quantum system;
a first manipulation sub-module configured to perform a transformation operation of said quantum state on M third quantum state components to obtain a second target quantum system, wherein said M third quantum states; The components include the first quantum state component and the M−1 target quantum state components, and the quantum state transform operation transforms the M first quantum states into M the second quantum states. a first manipulation sub-module comprising:
a second manipulation sub-module configured to perform a quantum state exchange operation on the second target quantum system to obtain a third target quantum system, wherein a second sub-quantum in the third target quantum system; The system includes M said second quantum states, said second sub-quantum system being arranged in front of M-1 third sub-quantum systems, said third sub-quantum systems being aligned with said third target A second operation sub-quantum system other than the second sub-quantum system in the quantum system, wherein the M-1 third sub-quantum systems and the M-1 first sub-quantum systems are the same a module;
a third manipulation sub-module configured to perform a reduction operation on the second sub-quantum system to obtain the target quantum state;
9. The convolution sub-module configured to convolute the quantum state components of each dimension in the M−1 third sub-quantum systems with uniform probability to obtain the auxiliary quantum state. Device. The second manipulation sub-module includes:
a first operation unit configured to take a dimension as a reference and perform a first rotation operation on quantum state components of each dimension in the second target quantum system to obtain a fourth target quantum system;
a second operation unit configured to take a sub-quantum system as a reference and perform a second rotation operation on each sub-quantum system in the fourth target quantum system to obtain the third target quantum system. 11. Apparatus according to claim 10. Specifically, the first operation unit
12. The apparatus according to claim 11, configured to rotate the quantum state components of each dimension in the second target quantum system according to ascending order of dimensions with a rotation step size of 1 to obtain a fourth target quantum system. . Specifically, the second operation unit
rotating each sub-quantum system in the fourth target quantum system with a rotation step size of 1 according to the front-to-back arrangement order of the sub-quantum systems to obtain the third target quantum system; 12. Apparatus according to claim 11. Specifically, the third operation sub-module:
removing the preset quantum states embedded in the M second quantum states to obtain a fourth sub-quantum system, the fourth sub-quantum system including M third quantum states; the third quantum state is a quantum state obtained after deleting the preset quantum state;
11. The apparatus of claim 10, configured to: convolute the M third quantum states with uniform probability to obtain the target quantum state. an electronic device,
at least one processor; and memory communicatively coupled to the at least one processor;
the memory stores instructions executable by the at least one processor;
An electronic device that causes the at least one processor to perform the method of any one of claims 1 to 7 when the instructions are executed by the at least one processor. A non-transitory computer-readable storage medium on which computer instructions are stored, said computer instructions being used to cause a computer to perform the method of any one of claims 1 to 7. computer readable storage medium. A computer program, comprising a computer program, for implementing the method of any one of claims 1 to 7 when said computer program is executed by a processor.

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